TA DAAaaaaaa!!!!! It's IN.
We already had to buy a new 'elbow'. I messed around so much with it, that I broke the airtight seal.
I took the pipe right out of the chimney, and attached it to the elbow, then shoved the whole thing, 'pre-assembled' stove and all, into the wall. The pipe that was supposed to fit OVER the other pipe actually ended up fitting the other way around. Small wonder I couldn't make it fit.